---
title: "An external force slowly stretches a non-linear elastic member along the \\(x\\)-axis from its equilibrium position at \\(x = 0\\). The magnitude of the stretching force \\(F\\) as a function of extension \\(x\\) is modeled by \\(F(x) = ax – bx^2\\), where \\(a\\) and \\(b\\) are positive constants, and is displayed in the calibrated graph. What is the total work done by the applied force to stretch the member from \\(x = 0\\) to \\(x = 0.20\\text{ m}\\)?"
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url: "https://nerd-notes.com/ubq/124106/"
date_modified: "2026-09-28T13:30:27+00:00"
---

# An external force slowly stretches a non-linear elastic member along the \(x\)-axis from its equilibrium position at \(x = 0\). The magnitude of the stretching force \(F\) as a function of extension \(x\) is modeled by \(F(x) = ax – bx^2\), where \(a\) and \(b\) are positive constants, and is displayed in the calibrated graph. What is the total work done by the applied force to stretch the member from \(x = 0\) to \(x = 0.20\text{ m}\)?

An external force slowly stretches a non-linear elastic member along the \(x\)-axis from its equilibrium position at \(x = 0\). The magnitude of the stretching force \(F\) as a function of extension \(x\) is modeled by \(F(x) = ax - bx^2\), where \(a\) and \(b\) are positive constants, and is displayed in the calibrated graph. What is the total work done by the applied force to stretch the member from \(x = 0\) to \(x = 0.20\text{ m}\)?

![A 2D Cartesian graph with a horizontal axis labeled x (m) and a vertical axis labeled F (N). The horizontal axis extends from 0 to 0.25 m with major tick marks and light gray gridlines at intervals of 0.05 m labeled 0, 0.05, 0.10, 0.15, 0.20, and 0.25. The vertical axis extends from 0 to 35 N with major tick marks and light gray gridlines at intervals of 5 N labeled 0, 5, 10, 15, 20, 25, 30, and 35. A single solid curve begins at (0, 0), arches upward as a concave-down parabola to a maximum at (0.10, 30), and descends symmetrically to intersect the horizontal axis at (0.20, 0). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602226-H673KC.jpg)

- **A.** \(4.0\text{ J}\)
- **B.** \(6.0\text{ J}\)
- **C.** \(8.0\text{ J}\)
- **D.** \(12\text{ J}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124106/*